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With the design of data communications in mind, 3GPP LTE-advanced (LTE-A) is probably the most promising technology for Internet of Things (IoT). For IoT applications, continuous low-rate streaming data may be reported from devices over a long period of time, imposing stringent requirements on power saving. To manage power consumption, 3GPP LTE-A has defined the discontinuous reception/transmission (DRX/DTX) mechanism to allow devices to turn off their radio interfaces and go to sleep in various patterns. Existing literature has paid much attention to evaluate the performance of DRX/DTX; however, how to tune DRX/DTX parameters to optimize energy cost is still left open. This paper addresses the DRX/DTX optimization, by asking how to maximize the sleep periods of devices while guarantee their quality-of-service (QoS), especially on the aspects of traffic bit-rate, packet delay, and packet loss rate in IoT applications. Efficient schemes to optimize DRX/DTX parameters and schedule devices' packets with the base station are proposed. The key idea of our schemes is to balance the impacts between QoS parameters and DRX/DTX configurations. Simulation results show that our schemes can guarantee traffic bit-rate, packet delay, and packet loss rate while save energy of user equipments .